LCM for 3, 7 and 8

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What's the Least Common Multiple (LCM) of 3, 7 and 8?

Answer

LCM of 3, 7 and 8 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 3 = 56, 168 ÷ 7 = 24, 168 ÷ 8 = 21 — and 56, 24 and 21 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/3 by 56 and of y/7 by 24 and of z/8 by 21.

3 — prime

7 — prime

8 = 23

Prime378Highest power
2——2323
33——3
7—7—7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
13721
23742
33721
34784
357105
36742
37721
378168
37963
3710210
3711231
371284
3713273
371442
3715105
3716336
3717357
3718126
3719399
3720420
372121
3722462
3723483
3724168
3725525
3726546
3727189
372884
3729609
3730210

FAQ

What's the Least Common Multiple (LCM) of 3, 7 and 8?

LCM of 3, 7 and 8 is 168

How to find the LCM of 3, 7 and 8 by prime factorization?

Take every prime that appears in 3, 7 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 3, 7 and 8 two numbers at a time?

Yes. The LCM of 3 and 7 is 21, and the LCM of 21 and 8 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 3, 7 and 8?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 3, 168 ÷ 7 and 168 ÷ 8 all come out whole. Any other common multiple of 3, 7 and 8 is a multiple of 168.

See Also